The present invention is described in the context of its application to analysis of private equity investment instruments, such as private equity funds. It will be appreciated by persons of ordinary skill in the art, however, that the methodology embodied in the present invention may be applicable to estimating expected cash flows from other investment instruments.
Private equity is the term used to describe a wide variety of investment strategies in companies that are not publicly traded. In most cases, private equity invests in companies that require capital to grow in excess of what their internally generated cash flow could achieve, but whose stage of development would not allow the companies to access the public debt or equity markets efficiently. Private equity investing also occurs when a disparity exists between the value ascribed by the market to a public company and the value that a private equity investor believes can be unlocked from the company if it were privately owned and managed. In this case, the investor attempts to buy the public shares of the company through a tender offer and de-list them, hoping to re-float the company at some future date at a greater value.
A private equity investment can take the form of debt, preferred equity, common equity, or any combination thereof, in a majority or a minority position, and represent an active or passive role in the management and direction of the company. As an asset class, private equity seeks to obtain high rates of return on invested capital as compared to the historical returns of the public markets. Private equity investors can invest in venture capital (VC) or private equity (PE) funds directly, or through a fund of funds structure. As the investments are identified at the underlying fund level the capital is called and the investments made.
The four stages of private equity investing are:                Own Capital and Friends & Family        Angel Investors        Venture Capital        Buyouts        
The stages are represented graphically in FIG. 1, and a brief description of each of the stages of private equity as an asset class is given below. It is worth mentioning, however, that the categories of private equity are dynamic in nature and the differences between them are often blurred. This is caused by the opportunistic nature of private equity investing.
Own Capital and Friends & Family
An entrepreneur starting a company usually taps his own sources of capital to help it grow. Once these sources dry up, approaching friends and family for additional capital usually follows.
Angel Investors
Angel Investors are wealthy individuals who seek to invest in new companies that have limited resources or financial or operational history. Angel Investors provide capital, Knowlege, experience and contacts to help the company grow. In return, they get an equity stake in the company and aim for financial returns in excess of 50% per year upon an event of liquidity. An event of liquidity is commonly referred to as an event that allows the investor to sell shares. This typically occurs when the company lists its shares in a public stock exchange or is sold to a third party.
Venture Capital
Venture Capital (VC) seeks to invest in companies having significant growth potential or require expansion capital. Many VC firms are specialized by industry and employ trained professionals to identify attractive business opportunities. VC firms invest their capital and provide industry knowledge and expertise in exchange for equity in the company. Typically, VC firms precondition their capital investment to having certain managerial and operational controls. These include hiring and firing key members of the management team, approving annual budgets and financial statements. Additionally, VCs have significant board representation. The VC industry is well organized and established; it is comprised of hundreds of finds. VC investors typically seek returns in excess of 25% per year at liquidity.
Buyouts
Buyouts (BO) seek to invest in companies that are typically more mature than those a VC would be interested in. These companies usually have significant financial or operational history, are most times cash flow positive and have assets that can be leveraged. As a result, BO firms can sometimes borrow to make their acquisitions more financially attractive. Similar to VC, BO firms can be specialized by industry and also employ trained professionals to identify attractive business opportunities. BO firms also invest capital and provide industry knowledge and expertise in exchange for equity, and often acquire controlling positions to actively manage their investments and maximize returns. BO can be further categorized by investing types, including leveraged buyouts (LBOs) and mezzanine. Like VC, BO is well organized and established, and is comprised of hundreds of funds. BO investors typically seek returns in excess of 25% per year at liquidity.
The participants in Private Equity include investors, general partners (GP's), and entrepreneurs/companies.
Investors
Investors in private equity are called Limited Partners (LPs) and include institutional investors and several wealthy individuals looking for diversification of their portfolios with an asset class that seeks high rates of return. Some of the largest investors in Private Equity (buyout) include pension funds, (CalPERS, CalSTRS), insurance companies (AIG, Prudential, etc.), and banks (CSFB, Deutsche Bank, etc.).
General Partners
General Partners (GP's) are the managers of the fund's assets. Their job is to seek, identify, and screen private equity investments. Additionally, they are expected to execute the investments on terms that are sufficiently attractive to ensure the fund's interests are protected and that a profitable exit through a successful liquidity event can be achieved.
Some of the best-known general partners in the VC segment include Kleiner, Perkins, Caufield & Byers, and Sequoia Capital. In the Private Equity (buyout) segment, some well-known names include Kohlberg, Kravis & Roberts, and Hicks, Muse Tate & Furst.
Entrepreneurs/Companies
Private equity identifies and provides capital to entrepreneurs and companies that show promise. As a result, it plays an important role in the development of a country's economy. Those countries with well-developed private equity industries, such as the US and the UK, are much more innovative and generally more dynamic than their counterparts.
Private equity also increases liquidity in the marketplace. As a result, risk can be transferred to those parties who are more willing to bear it without undue cost, making the economy more fluid and efficient.
Cashflow Patterns—J-Curves
Investments in private equity funds take the form of interests in the limited partnerships. Typically, that is represented in a commitment to invest a predetermined amount of cash over a certain time period.
Over time, GPs call (or draws down) the committed capital from the LPs pro-rata to their respective commitment amount to pay for management fees and, more importantly, to make investments or acquisitions in companies. GPs distribute capital (both return on capital and return of capital) back to the LPs when the companies in which they invested are sold. In the interim period between the investment and the distribution of cash, the GPs report the value of the investments on a quarterly basis. Unfortunately, the reported value for the underlying investments is not an accurate indicator of the actual value the investment would have if it were to be traded in the open market. As a result, the reported net asset value is largely ignored in analytics of expected private equity performance.
A typical private equity fund has a five-year draw down period and a five to seven year distribution period, both of which can be extended with consent from the LPs. In most funds, investments cannot be made after the drawdown period and the fund's life expires after the end of the distribution period. As a result, most funds are considered mature or fully liquidated after their 10-year anniversary.
The pattern followed by the cumulative drawdowns and distributions of cash into a fund over time is known as the fund's J-curve. An illustration of a typical J-curve is presented in FIG. 3, which is a plot of the data tabulated in FIG. 2. The year of inception of the private equity fund—and the corresponding J-curve—is referred to as the fund's vintage.
FIG. 2 shows a table for a hypothetical ten-year private equity fund. For each year of the fund's existence the incremental and cumulative drawdowns (“INC DD” and “CUMM DD”) are listed, as are the incremental and cumulative distributions (“INC DIS” and “CUMM DIS”). The difference between the cumulative distribution and the cumulative drawdown is the net cash flow (“NCF”). The values are listed as a percentage of the committed capital. That is, for a hypothetical investor, who, for example, has committed $10,000 to the private equity funds, the numbers listed in Table 2 are a percentage of that $10,000 commitment.
At year 0 (i.e., at the inception of the fund) there are, as yet, no drawdowns or distributions, and the net cash flow is zero. In year 1 of the hypothetical fund, the LP is asked to make an incremental payment (i.e., drawdown) of 20% of the committed capital. From a cash flow perspective, a drawdown is considered negative cash flow, and thus the drawdown is represented as −20%. In the hypothetical private equity fund illustrated in FIG. 2, the incremental distribution for year 1 is 1% (represented as positive cash flow). Thus, for year 1 the cumulative drawdown is −20%, the cumulative distribution is 1%, and the difference, or net cash flow, is −19%.
In year 2, the LP is requested to make a further payment, or drawdown, of an additional, or incremental, 25%. Thus, the cumulative drawdown after two years for that LP is 45%, represented as −45% cash flow. No incremental distribution is made in year 2 and thus the cumulative incremental distribution remains at 1% leading to a net cash flow of −44%.
In year 3, the incremental drawdown is 15% leading to a cumulative drawdown of −60% cash flow. The incremental distribution is 3 leading to a cumulative distribution of 4% cash flow, and the net cash flow is −56% (i.e., 4%-60%). In year 4, the incremental drawdown is 20% leading to a cumulative drawdown of −80% cash flow. The incremental distribution is 15% leading to a cumulative distribution of 19%, and the net cash flow is −61%.
In year 5, the incremental drawdown is 20% leading to a cumulative drawdown of −100% cash flow. The incremental distribution is 35% leading to a cumulative distribution of 54% and a net cash flow of −46%.
For years 6-10, there are no further drawdowns as the limited partner has now paid out 100% of the committed capital. Thus, for years 6-10 the cumulative drawdown remains at −100%. In year 6, the incremental distribution is 25% leading to a cumulative distribution of 79% and a net cash flow of −21%. In year 7, the incremental distribution is 35% leading to a cumulative distribution of 114% and a net cash flow of 14%. In years 8, 9, and 10, the incremental distributions are 32%, 22%, and 0, respectively, leading to cumulative distribution of 145%, 168%, and 168%, respectively, and net cash flows of 46%, 68%, and 68%.
FIG. 3 is a plot, i.e., the J-curve, of the net cash flow time series over the life of the private equity fund. The data points shown in FIG. 3 are those tabulated in FIG. 2.
Four important parameters of a J-curve include:
Money Multiple—is equal to total distributions divided by total contributions of capital. It is a measure of how profitably the capital has been invested from an absolute return perspective, without regard to the timing of the drawdowns or distributions. In the hypothetical private equity fund illustrated in FIGS. 2 and 3, the money multiple (MM) is 168/100=1.68
Internal Rate of Return—is the discount rate at which the present value of the draw downs equals the present value of the distribution. It is a measure of how profitably the capital has been invested from a temporal perspective without regard to the absolute returns achieved. Stated another way, in the context of the fund illustrated in FIGS. 2 and 3, what interest rate (i.e., internal rate of return) commencing at inception of the fund would pay 168% return on investment at the end of 10 years?
Speed of Draw—equals the number of periods for the J-curve to achieve its lowest point. It measures the relative speed at which the capital was drawn. In the fund illustrated in FIG. 3, the speed of draw is 4 periods.
Depth of Curve—equals the lowest point in the J-curve relative to the total amount of capital committed. It measures the relative amount of capital drawn before LPs began to receive distributions from their investments on a net basis (i.e. the investor may have received distributions in prior periods and may continue to be committed to make capital investments, but the investor will begin receiving a cumulative net amount of money greater than the capital that they need to invest from that point forward). In the fund illustrated in FIG. 3, the depth of fund is −61%.
When many funds are aggregated in an investment vehicle in what is known as a fund-of-funds structure, significant diversification can be achieved. Some of the most important parameters that can be diversified with a fund of funds structure include:
Operational diversificationJ-curve diversificationType of fundMoney multipleGeographyInternal rate of returnIndustrySpeed of drawFund's vintageDepth of curveManager
This diversification can be represented in J-curves as shown in FIG. 4.
As the example above illustrates, the depth of the J-curve is more favorable in the J-curve created from the cumulative net cash flows of each of the funds than in any of the individual J-curves.
Historical J-Curves and Cash Flow Modeling
The expected cash from a pool of private equity funds can be estimated by sampling individual J-curves of fully-liquidated vintages that have the same characteristics—such as, type of fund (e.g., buy-out or venture capital) and geographical focus (e.g., United States or Europe)—as each of the individual funds in the pool. The platform for making such estimations is known as a “private equity calculator.” The private equity calculator can be used in a variety of ways, including: securitizations (either a static or managed leveraged positions in a portfolio of hedge funds), regulatory risk capital assessments (optimization of the level of risk capital reserves required to maintain an investment in a pool of private equity funds); balance sheet risk management (identifying the volatility of the asset performance, and the timing and size of the contributions and distributions of cash); and investment management purposes (expected cash-on-cash performance or capital allocation optimization).
In the past, such estimations could be performed using complete J-curve data for available past vintages. For example, the net cash flow over the life of a private equity buy-out fund initiated in 2005 can be predicted by analyzing a number of the historical net cash flows (i.e., J-curves) for similar buy-out funds of fully liquidated vintages (e.g., 1980-1995). Such data had historically been provided by companies that provide reports and analysis regarding fund performance in the private equity industry, such as Venture Economics, a company owned by Thompson Financial. Recently however, for reasons relating to confidentiality of the various funds' data, complete J-curve data is no longer made available to the public. While the complete J-curve data is no longer available, statistics for the J-curves of different vintages are still made available. These statistics include: mean, median, and standard deviation statistics for of each of the four parameters that compose a J-curve (money multiple, internal rate of return, speed of draw, and depth of curve). Also, aggregate J-curve data for all similar funds (e.g., buy-out or venture capital) is available for each fully liquidated vintage year.
But, having only aggregate J-curve data and statistics for past vintage years is not sufficient for making predictions of future net cash flows for other funds. Accordingly, a need exists to provide equity fund cash flow estimates by simulating the J-curve data that is no longer publicly available.